A sum-of-squares-based procedure to approximate the Pontryagin difference of basic semi-algebraic sets

The P-difference between two sets A and B is the set of all points, C , such that the sum of B to any of the points in C is contained in A . Such a set difference plays an important role in robust model predictive control and set-theoretic control. In this paper, we show that an inner approximation of the P-difference between two sets described by collections of polynomial inequalities can be computed using Sums of Squares Programming. The effectiveness of the procedure is shown with some computational examples.